Reducibility of Killing tensors in d>4 NHEK geometry

TL;DR

This paper investigates the structure of hidden symmetries in higher-dimensional extremal rotating black holes, showing how certain Killing tensors relate to conformal symmetries in the near horizon geometry.

Contribution

It demonstrates that in arbitrary dimensions, one Killing tensor in NHEK geometry decomposes into conformal Killing vectors, revealing a reducibility property of hidden symmetries.

Findings

One Killing tensor decomposes into conformal Killing vectors.

Remaining Killing tensors are functionally independent.

The structure of symmetries is clarified in higher dimensions.

Abstract

An extremal rotating black hole in arbitrary dimension, along with time translations and rotations, possesses a number of hidden symmetries characterized by the second rank Killing tensors. As is known, in the near horizon limit the isometry group of the metric is enhanced to include the conformal factor SO(2,1). It is demonstrated that for the near horizon extremal Kerr (NHEK) geometry in arbitrary dimension one of the Killing tensors decomposes into a quadratic combination of the Killing vectors corresponding to the conformal group, while the rest is functionally independent.